Transverse sphericity of primary charged particles in minimum bias proton-proton collisions at $\sqrt{s}$=0.9, 2.76 and 7 TeV

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  EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH CERN-PH-EP-2012-136May 17, 2012 Transverse sphericity of primary charged particles in minimum biasproton-proton collisions at √  s = 0 . 9, 2 . 76 and 7 TeV The ALICE Collaboration ∗ Abstract Measurements of the sphericity of primary charged particles in minimum bias proton–proton colli-sions at √  s = 0 . 9, 2 . 76 and 7 TeV with the ALICE detector at the LHC are presented. The observableis linearized to be collinear safe and is measured in the plane perpendicular to the beam direction us-ing primary charged tracks with  p T ≥ 0 . 5 GeV/  c  in | η |≤ 0 . 8. The mean sphericity as a function of the charged particle multiplicity at mid-rapidity (  N  ch ) is reported for events with different  p T  scales(“soft” and “hard”) defined by the transverse momentum of the leading particle. In addition, the meancharged particle transverse momentum versus multiplicity is presented for the different event classes,and the sphericity distributions in bins of multiplicity are presented. The data are compared withcalculations of standard Monte Carlo event generators. The transverse sphericity is found to growwith multiplicity at all collision energies, with a steeper rise at low  N  ch , whereas the event generatorsshow the opposite tendency. The combined study of the sphericity and the mean  p T  with multiplicityindicates that most of the tested event generators produce events with higher multiplicity by generat-ing more back-to-back jets resulting in decreased sphericity (and isotropy). The PYTHIA6 generatorwith tune PERUGIA-2011 exhibits a noticeable improvement in describing the data, compared to theother tested generators. ∗ See Appendix A for the list of collaboration members   CERN-PH-EP-2012-13616 May 2012  Transverse sphericity of primary charged particles in MB proton-proton collisions 1 1 Introduction Minimum bias proton–proton collisions present an interesting, and theoretically, challenging subject fordetailed studies. Their understanding is important for the interpretation of measurements of heavy-ioncollisions, and in the search for signatures of new physics at the Large Hadron Collider (LHC) and Fer-milab. However, the wealth of experimental information is currently poorly understood by theoreticalmodels or Monte Carlo (MC) event generators, which are unable to explain with one set of param-eters all the measured observables. Examples of measured observables which are not presently welldescribed theoretically include the reported multiplicity distribution [1–3], the transverse momentum distribution [4] and the variation of the transverse momentum with multiplicity [5–7]. In this paper, we present measurements of the transverse sphericity for pp minimum bias events over awide multiplicity range at several energies using the ALICE detectors. Transverse sphericity is a momen-tum space variable, commonly classified as an event shape observable [8]. Event shape analyses, well known from lepton collisions [9–11], also offer interesting possibilities in hadronic collisions, such as the study of hadronization effects, underlying event characterization and comparison of pQCD computationswith measurements in high  E  T  jet events [12–14]. The goal of this analysis is to understand the interplay between the event shape, the charged particlesmultiplicity, and their transverse momentum distribution; hence, the present paper is focused on thefollowing aspects:– The evolution of the mean transverse sphericity with multiplicity for different subsets of eventsdefined by the transverse momentum of the leading particle;– the behavior of the mean transverse momentum as a function of multiplicity;– the normalized transverse sphericity distributions for various multiplicity ranges.The results of these analyses are compared with event generators and will serve for a better understandingof the underlying processes in proton-proton interactions at the LHC energies. 2 Event shape analysis At hadron colliders, event shape analyses are restricted to the transverse plane in order to avoid the biasfrom the boost along the beam axis [12]. The transverse sphericity is defined in terms of the eigenvalues: λ  1  >  λ  2  of the transverse momentum matrix: S Qxy  =  1 ∑ i  p T i ∑ i   p x2 i  p x i  p y i  p y i  p x i  p y2 i  where  (  p x i ,  p y i )  are the projections of the transverse momentum of the particle  i .Since  S Qxy  is quadratic in particle momenta, this sphericity is a non-collinear safe quantity in pQCD. Forinstance, if a hard momentum along the  x  direction splits into two equal collinear momenta, then thesum  ∑ i  p x2 i  will be half that of the srcinal momentum. To avoid this dependence on possible collinearsplittings, the transverse momentum matrix is linearized as follows: S Lxy  =  1 ∑ i  p T i ∑ i 1  p T i   p x2 i  p x i  p y i  p y i  p x i  p y2 i   2 The ALICE CollaborationThe transverse sphericity is defined as S  T ≡  2 λ  2 λ  2  + λ  1 .  (1)By construction, the limits of the variable are related to specific configurations in the transverse plane S  T  =  {  =  0 “pencil-like” limit =  1 “isotropic” limit  . This definition is inherently multiplicity dependent, for instance,  S  T → 0 for very low multiplicity events. 3 Experimental conditions The relevant detectors used in the present analysis are the Time Projection Chamber (TPC) and the InnerTracking System (ITS), which are located in the central barrel of ALICE inside a large solenoidal magnetproviding a uniform 0 . 5 T field [15].The ALICE TPC is a large cylindrical drift detector with a central membrane maintained at -100 kVand two readout planes at the end-caps composed of 72 multi-wire proportional chambers [17]. Theactive volume is limited to 85  <  r   <  247 cm and  − 250  <  z  <  250 cm in the radial and longitudinaldirections, respectively. The material budget between the interaction point and the active volume of theTPC corresponds to 11% of a radiation length, averaged in | η |≤ 0 . 8. The central membrane divides thenearly 90  m 3 active volume into two halves. The homogeneous drift field of 400 V/cm in the Ne-CO 2 -N 2 (85.7%-9.5%-4.8%) gas mixture leads to a maximum drift time of 94  µ  s. The typical gas gain is 10 4 [7].The ITS is composed of high resolution silicon tracking detectors, arranged in six cylindrical layersat radial distances to the beam line from 3.9 to 43 cm. The two innermost layers are Silicon PixelDetectors (SPD), covering the pseudorapidity ranges | η | < 2 and | η | < 1.4, respectively. A total of 9.8millions 50 × 425  µ  m 2 pixels enable the reconstruction of the primary event vertex and the track impactparameters with high precision. The SPD was also included in the trigger scheme for data collection. Theouter third and fourth layers are formed by Silicon Drift Detectors (SDD) with a total of 133k readoutchannels. The two outermost Silicon Strip Detector (SSD) layers consist of double-sided silicon micro-strip sensors with 95  µ  m pitch, comprising a total of 2.6 million readout channels. The design spatialresolutions of the ITS sub-detectors ( σ  r  φ  × σ   z ) are: 12 × 100  µ  m 2 for SPD, 35 × 25  µ  m 2 for SDD, and20 × 830  µ  m 2 for SSD. The ITS has been aligned using reconstructed tracks from cosmic rays and fromproton-proton collisions [16].The VZERO detector consists of two forward scintillator hodoscopes. Each detector is segmented into32 scintillator counters which are arranged in four rings around the beam pipe. They are located atdistances  z  =  3 . 3 m and  z  = − 0 . 9 m from the nominal interaction point and cover the pseudorapidityranges: 2 . 8  <  η  <  5 . 1 and − 3 . 7  <  η  < − 1 . 7, respectively. The beam-related background was rejectedat offline level using the VZERO time and by cutting on the correlation between the number of clustersand track segments in the SPD.The minimum bias (MB) trigger used in this analysis required a hit in one of the VZERO counters or inthe SPD detector. In addition, a coincidence was required between the signals from two beam pickupcounters, one on each side of the interaction region, indicating the presence of passing bunches [1]. 4 Data analysis MB events at  √  s  =  0.9 and 7 TeV (recorded in 2010) and at  √  s  =  2 . 76 TeV (recorded in 2011) havebeen analyzed using about 40 million events, each at 7 and 2.76 TeV, and 3.6 million at 0.9 TeV. Sinceno energy dependence is found for the event shape observable, we present mostly results for 0.9 and 7TeV.  Transverse sphericity of primary charged particles in MB proton-proton collisions 3The position of the interaction vertex is reconstructed by correlating hits in the two silicon-pixel layers.The vertex resolution depends on the track multiplicity, and is typically 0 . 1 − 0 . 3 mm in the longitudinal(  z ) and 0 . 2 − 0 . 5 mm in the transverse direction. The event is accepted if its longitudinal vertex position(  z v ) satisfies |  z v −  z 0 | <  10 cm, where  z 0  is the nominal position.To ensure a good resolution on the transverse sphericity, only events with more than two primary tracksin | η |≤ 0 . 8 and  p T ≥ 0 . 5 GeV/  c  are selected. The cuts on  η  and  p T  ensure high charged particle track reconstruction efficiency for primary tracks [7]. These cuts reduce the available statistics to about 9 . 1,4 . 2 and 0 . 42 million of MB events for the 7 TeV, 2.76 TeV and 0.9 TeV data, respectively.At 7 TeV collision energy, the fractions of non-diffractive events after the cuts are 99 . 5% and 93 . 6%according to PYTHIA6 version 6.421 [18] (tune PERUGIA-0 [19]) and PHOJET version 1.12 [20], respectively. In the case of single-diffractive events the fractions are 0 . 3% and 4 . 8%, while the double-diffractive events represent 0 . 2% and 1 . 6% of the sample as predicted by PYTHIA6 and PHOJET, re-spectively. 4.1 Track selection Charged particle tracks are selected in the pseudorapidity range  | η |≤ 0 . 8. In this range, tracks in theTPC can be reconstructed with minimal efficiency losses due to detector boundaries. Additional qualityrequirements are applied to ensure high tracking resolution and low contamination from secondary andfake tracks [7]. A track is accepted if it has at least 70 space points in the TPC, and the  χ  2 per spacepoint used for the momentum fit is less than 4. Tracks are rejected as not associated to the primaryvertex if their distance of closest approach to the reconstructed event vertex in the plane perpendicularto the beam axis,  d  0 , exceeds 0 . 245 +  0 . 294  p 0 . 9T (  p T  in GeV/  c ,  d  0  in cm). This cut is tuned to select primarycharged particles with high efficiency and to minimize the contributions from weak decays, conversionsand secondary hadronic interactions in the detector material. 4.2 Selection of soft and hard events The analysis is presented for two categories of events defined by the maximum charged-particle trans-verse momentum for  | η |≤ 0 . 8 in each event. This method is often used in an attempt to characterizeevents by separating the different modes of production. It aims to divide the sample into two eventclasses: a) events dominantly without any hard scattering (“soft” events) and b) events dominantly withat least one hard scattering (“hard” events). Figure 1 shows the mean transverse sphericity versus maxi-mum  p T  of the event obtained from minimum bias simulations at √  s = 7 TeV using the particle and eventcuts described previously. Note that PYTHIA6 simulations (tunes: ATLAS-CSC [21], PERUGIA-0 and PERUGIA-2011[22])exhibitamaximumaround1 . 5 − 2 . 0GeV/  c , whilePHOJETshowsanintermediatetransition slope in  p maxT  = 1 − 3 GeV/  c . This observation motivated the choice of the following separationcut: “soft” events are defined as events that do not have a track above 2 GeV/  c , while “hard” events areall others. The aggregate of both classes is called “all”. The selection of 2 GeV/  c  has been motivatedin the past as an accepted limit between soft and hard processes [23]. For parton-parton interactionsthe differential cross section is divergent for  p T → 0, so that a lower cut-off is generally introduced inorder to regularize the divergence. For example in PYTHIA6, the default cut-off is 2 GeV/  c  for 2 → 2processes.Table1showstheratioof“soft”to“hard”eventsforALICEdataandthegenerators: PHOJET,PYTHIA6(tunes ATLAS-CSC, PERUGIA-0 and PERUGIA-2011) and PYTHIA8 version 8.145 [24]. It illustratesthe difficulties to reproduce the evolution of simple observables with collision energy.
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